A346253 a(n) = A342002(A328623(n)).

0, 1, 2, 7, 1, 5, 3, 11, 19, 53, 14, 43, 1, 7, 13, 41, 8, 31, 4, 13, 22, 59, 17, 49, 2, 9, 16, 47, 11, 37, 4, 15, 26, 73, 19, 59, 41, 117, 193, 491, 158, 421, 27, 89, 151, 407, 116, 337, 48, 131, 214, 533, 179, 463, 34, 103, 172, 449, 137, 379, 1, 9, 17, 55, 10, 41, 26, 87, 148, 401, 113, 331, 12, 59, 106, 317, 71, 247, 33, 101, 169

Offset: 0

Author

Antti Karttunen, Jul 11 2021

Keywords

• nonn
• base
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..13860
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A003557, A328623, A342001, A342002, A346233.

Cf. also A344760, A346252.

Programs

PARI

A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A346253(n) = A342002(A328623(n)); \\ Rest of program in A328623.

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
A346233(n) = { my(p=2, m=1); while(n>0, my(d=n%p); if(d>0, m *= p^if(2==p,d,lift(Mod(d, p)/2))); n \= p; p = nextprime(1+p)); return(m); };
A346253(n) = A342001(A346233(n));

Formula

a(n) = A342001(A346233(n)) = A342002(A328623(n)).